Adagio KV540 - 55ED2
14 December 2011 Filed in: Music
Listen to Adagio in B minor KV540 by W. A. Mozart
I used to play this piece, when I considered myself a pianist.
Now, being an electronic musician with a penchant for microtonal tuning systems, I have revisited this marvelous piece from a different perspective.
I happened to listen to it after a long time and it reminded me of a book I had read: “How equal temperament ruined harmony (and why you should care)” by Ross W. Duffin. The author mentions a tuning system that Mozart knew for sure and very likely appreciated. It is an equal temperament, similar to a meantone tuning system: 55ED2 (a.k.a. 55EDO) that is very close to 1/6 comma meantone. I decided to use this tuning system for my version of this piece.
The dodecatonic scale based on 55ED2 has a large and a small semitone.
The large one (L) measures 5 commas and the small one (s) 4 commas where one comma is 1/55 of an octave (21.818 cents), so, L = 109.091 cents and s = 87.273 cents.
One tone is the sum of L + s, 9 commas or 196.364 cents.
One octave is composed of 5 tones plus two large semitones:
(5 * 9 + 2 * 5 = 55).
The idea is that a diatonic semitone, from D to Eb, for example, is one comma larger than a chromatic semitone, from D to D#.
This piece is in B minor (the relative minor of D major) so I created the following scale based on D:
D, Eb, E, F, F#, G, G#, A, Bb, B, C, C#, D or (measured in commas):
5, 4, 5, 4, 5, 4, 5, 5, 4, 5, 4, 5
I noticed this scale was formed by two disjunct tetrachords:
(5, 4, 5, 4, 5) 4, 5 (5, 4, 5, 4, 5) and I took it as a good sign.

I also decided that the frequency of the root note of the piece (D) should be 32 commas (a compressed fifth of 698.182 cents) below an A tuned to 415Hz. LMSO did the calculation for me and gave me the result of 277.27 Hz (everlasting praise to X.J.Scott).
The best piano sound I have at my disposal is the one of my Nord Stage Classic 88 Rev. C. I have never used its sounds for microtonal music because of its shortcomings: the piano section can not receive on more than two MIDI channels at the same time and that, for retuning technology based on pitch bend, means a maximum of two notes polyphony. This piece calls for a maximum of five notes polyphony (no sustain pedal is ever used).
The realization of this piece was done in a few steps:
1) I played it, in 12tET, few bars at the time, at a steady tempo, making sure to play with the right articulation and dynamics.
2) I imported the audio file of the performance of this piece by a famous pianist, I will not name, into Logic Pro and used it as reference to create a tempo list with the beat mapping function.

Here you can see the first three bars of the piece. The idea is to align the beat position of the MIDI track to the detected transients of the audio file used as reference. It has to be done by hand, one at the time! But in the end it is possible to create a MIDI performance that really “breaths”!
The tempo list created this way was then edited to my taste.
My version does not include the two refrains written on the score. Instead of a form AABBC (where C is the short finale) I play the form ABC, but the version I used as reference plays AABC. So I also had to cut and paste the tempo list based on it to adapt it to my version.
3) In order to retune the piece to be played by the NS88 I edited the two MIDI tracks (right hand and left hand) I had recorded, assigning MIDI channel 1 to all the notes that could be played by a duophonic instrument and assigning MIDI channel 2 every time I had a third simultaneous note. I then proceeded to send MIDI notes, one track at the time, to LMSO, to retune them to 55ED2.

Assigning MIDI channel 1 as the LMSO input I made sure not to exceed the maximum two notes polyphony available to retune the NS88.

So, I recreated the piece, now retuned to 55ED2, recording three audio tracks: the first one playing notes on channel 1 of the right hand track, the second one playing notes on channel 1 of the left hand track and the third one playing notes on channel 2 of both MIDI tracks.
This way I overcame the NS88’s shortcomings. I then added some effects (reverb and compression) and that was it.
As comparison I present the same piece tuned to 12ED2 and A = 440 Hz:
Listen to Adagio in B minor KV540 - 12ED2 by W. A. Mozart